I saw a Cook Islands tourism ad, and the English spoken there seemed very similar to New Zealand English. For example, the accent, and the use of "bro". (The sense of humour is also very similar to that of New Zealand, such as John Clarke's). This wouldn't be surprising, as the Cook Islands are in free association with New Zealand.
However, Paradise or Gloucester? The Pacific islanders who all speak with a West Country accent on Daily Mail Australia (not the most reliable source, I know), cites a researcher who associates the accent with the West Country in the UK, and apparently has no mention of New Zealand English. (I assume that if New Zealand English is also influenced by that of the West Country, it'd have been mentioned)
Is the English spoken in the Cook Islands similar to New Zealand English?
Searching for "Cook Islands English" mainly gave matches unrelated to the concept of the version of English spoken in the Cook Islands.